---
title: "Graphing Residuals"
date: 'Last compiled: `r format(Sys.time(), "%A, %B %d, %Y - %X.")`'
author: 'Alan T. Arnholt'
output: 
    bookdown::html_document2
---

```{r label = "setup", include = FALSE, message = FALSE}
library(ggplot2)
knitr::opts_chunk$set(echo = TRUE, comment = NA, fig.align = "center", warning = FALSE, message = FALSE)
```

# (APPENDIX) Appendix A {-}

## Residuals

The $i^{th}$ residual is defined as $\hat{\epsilon}_i = y_i - \hat{y}_i$.


```{r}
library(dplyr)
library(PASWR2)
head(HSWRESTLER)
mod_null <- lm(hwfat ~ 1, data = HSWRESTLER)
summary(mod_null)
anova(mod_null)
HSWRESTLER %>% 
  summarize(Intercept = mean(hwfat))
mod_slr <- lm(hwfat ~ abs, data = HSWRESTLER)
summary(mod_slr)
anova(mod_slr)
```

* Use the function `augment` from the `broom` package

```{r}
library(broom)
mod_slr %>% 
  augment() %>% 
  head() %>% 
  round(3)
NDF1 <- mod_slr %>% 
  augment()
NDF2 <- mod_null %>% 
  augment()
NDF2$abs <- HSWRESTLER$abs
```

## Graphing

### Residuals for SLR model

```{r}
ggplot(data = NDF1, aes(x = abs, y = hwfat)) + 
  geom_point(color = "purple") + 
  theme_bw() + 
  geom_line(aes(x = abs, y = .fitted), color = "gray") + 
  geom_segment(aes(x = abs, xend = abs, y = hwfat, yend = .fitted), size = 0.25)
```

### Residuals for Null model

```{r}
ggplot(data = NDF2, aes(x = abs, y = hwfat)) + 
  geom_point(color = "purple") + 
  theme_bw() + 
  geom_line(aes(x = abs, y = .fitted), color = "gray") + 
  geom_segment(aes(x = abs, xend = abs, y = hwfat, yend = .fitted), size = 0.25)
```

### Creating one dataframe with new column

The code below creates one dataframe (`ndf`) with the information from the `null` model appended to the bottom of the information from the `slr` model.

```{r}
ndf1 <- augment(mod_slr)
ndf2 <- augment(mod_null)
DT::datatable(head(ndf1))
DT::datatable(head(ndf2))
ndf2$abs <- HSWRESTLER$abs  # Note that abs is not in ndf2....so must add
ndf <- bind_rows(ndf1, ndf2) %>% 
  mutate(model = rep(c("slr", "null"), each = 78)) 
DT::datatable(ndf)
```

```{r, fig.width = 8}
ggplot(data = ndf, aes(x = abs, y = hwfat)) +
  facet_grid(.~ model) + 
  geom_line(aes(x = abs, y = .fitted), color = "gray") + 
  theme_bw() + 
  geom_segment(aes(x = abs, xend = abs, y = hwfat, yend = .fitted), size = 0.25, linetype = "dotted") + 
  geom_point(color = "lightblue") 
```
The graph above is created with a Figure Caption and hidden code in Figure \@ref(fig:BG).


### Tweakers 

Note that `mod_null` and `mod_slr` are  lists with the results from the `lm` call.

```{r}
str(mod_null)
str(mod_slr)
```

Consider the following:

```{r}
mod_null <- mod_null %>% augment()
mod_null$abs <- HSWRESTLER$abs
mod_slr <- mod_slr %>% augment()
```

```{r}
DT::datatable(mod_null)
```

* Compute the mean squared error ($MSE$) for the null model `mod_null`.

```{r}
# Compute SSE for null model
mod_null %>%
  summarize(MSE = var(hwfat))
```

* Compute the mean squared error ($MSE$) for the regression model `mod_slr`.

```{r}
# Compute SSE for regression model
mod_slr %>%
  summarize(MSE = var(.resid))
```

## Graph with caption

```{r, label = "BG", echo = FALSE, fig.cap = "What you want your caption to say goes here", fig.width = 8}
mod_null <- lm(hwfat ~ 1, data = HSWRESTLER)
mod_slr <- lm(hwfat ~ abs, data = HSWRESTLER)
ndf1 <- augment(mod_slr)
ndf2 <- augment(mod_null)
ndf2$abs <- HSWRESTLER$abs  # Note that abs is not in ndf2....so must add
ndf <- bind_rows(ndf1, ndf2) %>% 
  mutate(model = rep(c("slr", "null"), each = 78)) 
mod_null <- mod_null %>% augment()
mod_slr <- mod_slr %>% augment()
ggplot(data = ndf, aes(x = abs, y = hwfat)) +
  facet_grid(.~ model) + 
  geom_line(aes(x = abs, y = .fitted), color = "gray") + 
  theme_bw() + 
  geom_segment(aes(x = abs, xend = abs, y = hwfat, yend = .fitted), size = 0.25, linetype = "dotted") + 
  geom_point(color = "blue") 
```